Royal Flush odds

[Sardis]

To those that know......

I was playing in a live Hold Em tournament last night and the flop came Ah Kh Qh Jh Th (not in that order).

What are the odds of flopping a royal flush ? And what's the logic for the calculation ?

What's the best book on poker related probabilty calculations ?

Any help much appreciated .....

Sardis

[tworooks]

[ QUOTE ]
the flop came Ah Kh Qh Jh Th

[/ QUOTE ]
awkward, the hold'em that i play we only get 3 cards on the flop

[Sardis]

Tworooks,

OK...


The board came Ah Kh Qh Jh Th.....

[closer2313]

Well the odds of flopping a royal flush assuming you have 2 suited broadway cards are.

1/C(50,3) ~ 0.00510204082% or 19599:1 against

For the board to be a royal should be:
Assuming you know your 2 hole cards and neither of them are an Ace,King,Queen,Jack,Ten then its

4/C(50,5)~0.000188789669% or 529,689:1 against

[Jeoke]

Could you possibly write out that equation more in depth for me? I have to do some stupid math presentation and want to do the odds of getting a Royal Flush. Thanks

[Jacob_Gilliam]

to complete your royal, on the first card you have a 20/50 chance to get a card that starts a royal (given you dont hold any 10's through A's), next card 4/49 to continue with the royal, then 3/48, then 2/47, then 1/46.multiply all those numbers together (20/50 x 4/49 x 3/48 x 2/47 x 1/46) and you have your answer.

[imported_anacardo]

So did you push?

[Jeoke]

what if you have 2 of the cards in your hand?

sorry if this is hijacking, but to me it fits in with the original post

[blaze666]

http://www.google.co.uk/search?hl=en&q=royal+flush+odds&meta=


the odds are the same in draw methinks, seing as it is just the same as a 5 card hand so that 1 in 649,750 hands will a royal come on the flush. that is also the chances of it being dealt to you in 5 card draw.

[LetYouDown]

That should be 649740, not 649750.

The difference is, he was assuming that the person in question didn't have any broadway cards.

Therefore, instead of 4/52 C 5, it becomes 4/50 C 5.

529689 to 1 is the correct answer in that case.

[LetYouDown]

If you have two suited broadway cards, the odds that the board will come a royal flush in any other suit should be:

3/50 C 5 or roughly 706252 to 1.

If you have two unsuited broadway cards, the odds just drop to:

2/50 C 5 or 1,059,379 to 1.

[Jeoke]

[ QUOTE ]
If you have two suited broadway cards, the odds that the board will come a royal flush in any other suit should be:

3/50 C 5 or roughly 706252 to 1.

If you have two unsuited broadway cards, the odds just drop to:

2/50 C 5 or 1,059,379 to 1.

[/ QUOTE ]

I'm new to this forum and I dont know what 2/50 C means. Could you please explain to me.

I would love to know how to figure out the chances(in a way i can understand) of getting a royal flush by the time the river comes while holding 2 suited broadway cards. I know how to figure it would 5 cards in a row but what about when there are usless cards inbetween. for example, the board comes out 6s Ah 8d Kh Qh when you hold 10h Jh.

Would it me.. (3/50)(3/49)(2/48)(2/47)(1/46)= .000014159 or 7062532 to 1?

Thanks for any help

[LetYouDown]

Well, you need 3 exact cards...no matter what.

There are C(50,5) possible boards that can come. This translates to the fact that there are 50 cards remaining in the deck and 5 of them must be chosen. To calculate this, you do:

50!
---------
5!(50-5)!

This comes out to be 2118760 possible boards (regardless of order), when you hold two cards.

Because you know you'll end up with a royal flush, you know 3 of these cards. So now you have C(47,2) because you need to fill the other spots on the board. This will get you the number of combinations that contain the 3 cards you need. Then it's simple division.

C(47,2) = 1081

1081 boards contain your royal flush cards
There are 2118760 possible boards.

So it looks like 1081/2118760...or 1959 to 1 to me.

[Jacob_Gilliam]

In my earlier example, if you have one broadway or two suited broadways, the first number gets changed from 20/50 to 15/50 (because a royal in one suit is impossible on the board). If you have two different broadways, change the first number to 10/50 (two different royals on the board are impossible).

[Sardis]

Hey thanks guys...

Indeed the event was a royal flush on the board..I had no card holding.

And yes I pushed /images/graemlins/smile.gif

Guess it's going to be a while. 528,689 hands till I see this again. Assuming I play 44 hands / hr and play for an average of 4 hrs aweek... I think thats 56 plus yrs before I'll see this again in 2061 (I'll be 112 yrs old).

Cool

/images/graemlins/smile.gif

Sardis

[Dex]

[ QUOTE ]
Hey thanks guys...

Indeed the event was a royal flush on the board..I had no card holding.

And yes I pushed /images/graemlins/smile.gif

[/ QUOTE ]

Did anyone fold? /images/graemlins/grin.gif